The approaches described in this section are approaches that could be pursued, but not necessarily approaches that have been previously conceived or pursued. Therefore, unless otherwise indicated, it should not be assumed that any of the approaches described in this section qualify as prior art merely by virtue of their inclusion in this section.
A time series is a sequence of data points that are typically obtained by capturing measurements from one or more sources over a period of time. As an example, businesses may collect, continuously or over a predetermined time interval, various performance metrics for software and hardware resources that are deployed within a datacenter environment. Analysts frequently apply forecasting models to time series data in an attempt to predict future events based on observed measurements. One such model is the Holt-Winters forecasting algorithm, also referred to as triple exponential smoothing.
The Holt-Winters forecasting algorithm takes into account both trends and seasonality in the time series data in order to formulate a prediction about future values. A trend in this context refers to the tendency of the time series data to increase or decrease over time, and seasonality refers to the tendency of time series data to exhibit behavior that periodically repeats itself. A season generally refers to the period of time before an exhibited behavior begins to repeat itself. The additive seasonal model is given by the following formulas:Lt=α(Xt−St−p)+(1−α)(Lt−1+Tt−1)  (1)Tt=γ(Lt−Lt−1)+(1−γ)Tt−1  (2)St=δ(Xt−Lt)+(1−δ)St−p  (3)where Xt, Lt, Tt, and St denote the observed level, local mean level, trend, and seasonal index at time t, respectively. Parameters α, γ, δ denote smoothing parameters for updating the mean level, trend, and seasonal index, respectively, and p denotes the duration of the seasonal pattern. The forecast is given as follows:Ft+k=Lt+kTt+St+k-p  (4)where Ft+k denotes the forecast at future time t+k.
The additive seasonal model is typically applied when seasonal fluctuations are independent of the overall level of the time series data. An alternative, referred to as the multiplicative model, is often applied if the size of seasonal fluctuations vary based on the overall level of the time series data. The multiplicative model is given by the following formulas:Lt=α(Xt/St−p)+(1−α)(Lt−1+Tt−1)  (5)Tt=γ(Lt−Lt−1)+(1−γ)Tt−1  (6)St=δ(Xt/Lt)+(1−δ)St−p  (7)where, as before, Xt, Lt, Tt, and St denote the observed level, local mean level, trend, and seasonal index at time t, respectively. The forecast is then given by the following formula:Ft+k=(Lt+kTt)St+k-p  (8)
Predictive models such as triple exponential smoothing are primarily focused on generating forecasts about future events. While the Holt-Winter additive and multiplicative models take into account seasonal indices to generate the forecast, these models provide limited information on any seasonal patterns that may exist in the time series data. In particular, the seasonal indices represented by equations (3) and (7) are typically implemented as internal structures that operate within the bounds of the forecasting models to which they are tied. As a result, the seasonal data output by these formulas does not lend itself to meaningful interpretation in contexts outside of the specific forecasting models for which the seasonal data was generated. Further, the end user may have little or no underlying notion of any seasonal data that was used in generating a forecast.